The force has urged people to contact them immediately if they spot the blue case.
Police also raided a building in a southern Manchester suburb and another in the city of Chester in connection with last week's attack on an Ariana Grande concert by Salman Abedi, a 22-year-old Briton of Libyan descent.
Jackson added, "I want to stress that this is a different item than the one he used in the attack".
People look at flowers and balloons in St Ann's Square yesterday, placed in tribute to the victims of the May 22 terror attack at the Manchester Arena.
Officers are asking members of the public if they saw Salman Abedi with the suitcase between May 18 and May 22, when he carried out the attack.
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A United Kingdom security official told The Wall Street Journal Monday that suicide bomber Salman Abedi, who massacred 22 people at an Ariana Grande concert in Manchester on May 22 via a bomb in his backpack full of metal screws, was known to MI5 but not under active investigation.
Police investigating the suicide attack in Manchester are searching a landfill site on the outskirts of Bury.
"Our inquiries show Abedi himself made most of the purchases of the core components and what is becoming apparent is that many of his movements and actions have been carried out alone during the four days from him landing in the country and committing this bad attack".
Authorities say Abedi returned to Britain from Libya on May 18, and likely completed assembling his bomb at a rented apartment in central Manchester.
Fourteen men are now detained on United Kingdom soil in the investigation, while Abedi's father and brother have been held in Libya, where officials said the two brothers were IS jihadists.
Investigators said they have a 1,000-strong team working on the probe and have significant details on Abedi's associates and movements, his finances, and how the bomb was built.
On Sunday, two men were arrested in Manchester - a 19-year-old man in Gorton and a 25-year-old man in the Old Trafford area.